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Twelve of the 20 students in Ms. Sarno’s homeroom are female. Each month, Ms. Sarno randomly selects a student to act as “teacher’s helper.”

Which simulation best models the selection of female “teacher’s helpers” for January, February, March, and April?
A spinner, divided into 5 congruent sectors with three of the sectors representing female students, is spun 12 times.
A coin, with heads up representing female students, is flipped 4 times.
A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.
A number cube, with odd numbers representing female students, is rolled 12 times.

1 answer

To determine which simulation best models the selection of female "teacher’s helpers" for January, February, March, and April, we need to consider how many female students there are and how many months we are simulating.

Ms. Sarno's homeroom consists of 20 students, of which 12 are female. This means the probability of selecting a female student is 12 out of 20, or 60%. We are interested in simulating 4 selections (one for each month from January to April).

Now, let's analyze the given options:

  1. A spinner, divided into 5 congruent sectors with three of the sectors representing female students, is spun 12 times.

    • This option suggests spinning the spinner 12 times, which is unnecessary since we only need to make 4 selections. Therefore, it doesn't model the scenario correctly.

  2. A coin, with heads up representing female students, is flipped 4 times.

    • A coin has an equal chance of landing heads or tails, which does not simulate the probability of selecting a female student (60% likelihood). Thus, this option is not appropriate.

  3. A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.

    • This option represents the correct setup. With 9 out of 15 marbles representing female students, it aligns with the relative probability of selecting students. Drawing 4 times simulates the selection for January, February, March, and April, and doing so with replacement reflects the fact that each month's selection is independent of the others.

  4. A number cube, with odd numbers representing female students, is rolled 12 times.

    • A standard number cube (die) has 6 sides, and using odd numbers to represent students doesn’t correctly represent the ratio of female students. Additionally, rolling the die 12 times is not relevant to the scenario, which only requires 4 selections.

Among these options, the one that best models the selection of female "teacher’s helpers" for the four months is:

A bag of 15 marbles, with 9 marbles representing female students, has a marble drawn 4 times with replacement.